A 100km stretch of beach from St-Raphaël to the Italian border, the Côte d'Azur is holiday heaven. International celebrities have long flocked to Cannes, British families to Antibes. But it was French tourists, perennial visitors to dozens of lower-key Riviera resorts, who turned me on to the Carte Isabelle rail pass and the secret of seeing it all in a single day.

Costing a bargain €12 (£10), this day-long rail pass allows unlimited travel on any of the half-hourly trains that scoot along France's Mediterranean shoreline. There are 30 super-cute stations between historic Fréjus and the Italian border town of Ventimiglia. On a summer's day, it was a challenge: Carte Isabelle in hand, how many could I hit?

Trains begin trundling along the coast around 5.30am. Although I'm itching to make the most of a day on the rails, it's a shade early for me. Instead I pitch up at Nice-Ville, the city's main train station, in time for a 7.53am departure to Ventimiglia.

This sunny corner of France breeds late risers. As the train shudders eastwards, I'm one of the few Riviera residents enjoying the mirrorlike seascapes from the train's giant picture windows. Sharing my carriage is a handful of commuters; after they get off in Monaco, I'm riding solo. We race over the border – no passport control here – pulling into the rail pass's only Italian destination to a chorus of ciaos and grazies at 8.42am.

The day is heating up. The Riviera basks in 300 days of sunshine a year, and it's hot and sultry from May onwards. I need to get my head under water and alight on a whim at Roquebrune for the Plage de la Buse, a sandy beach set underneath Coco Chanel's sumptuous former home, Villa La Pausa. Down a stone staircase is the public beach, where kids are building giant sandcastles and Monaco's skyscrapers hang on the horizon. Around the bay's eastern bend, Swiss architect Le Corbusier's former studio Le Cabanon peeks out through Aleppo pines.

After a splash in the sea, I hike back uphill to catch the 11.06am, hopping off a mere seven minutes later at Monaco, my third country in as many hours. I make a beeline for the Place du Casino. Littered with fluffy white lapdogs and oodles of bling, the square is defined by my favourite holiday snapshot: a group of tourists all photographing each other wearing cameras in front of the parked Ferraris.

But the Riviera is not only for the super-rich, as proved by lunch at Café Llorca (Grimaldi Forum, 10 avenue Princesse Grace). Michelin-starred chef Alain Llorca opened this bright, modern bistro at the end of 2010, but the menu is a penny pincher's dream: my plat du jour – red mullet terrine with salad – costs €11.

A sandy cove at Cap d’Ail, accessible only on foot.

I hustle back to the station as the 13.43 pulls in. From my window seat turquoise inlets alternate with isolated sandy coves as the seaside enclaves roll by: cool Cap d'Ail, accessible only on foot and renowned for its brilliant snorkelling, then Eze-sur-Mer, famed for its sheltered bay and Bono's sprawling holiday home. At 13.56, I alight once again, this time at Beaulieu-sur-Mer.

It's about 15 minutes on foot between most destinations on the Carte Isabelle rail-pass line, so I walk westwards to the next station. A stroll past several public beaches takes me along the foot of Europe's wealthiest peninsula, Cap Ferrat. From here a public sentier du littoral, or coastal walking path, ribbons south to David Niven's former home, its pink facade visible from the shore. I cut right across the Cap's base, stopping to peek through the iron gates of Villa Nellcôte, Keith Richards's 1970s palace of debauchery, where the Rolling Stones recorded Exile on Main Street.

Then it's on to Villefranche-sur-Mer's deep bay, its image made famous in Mr Bean's Holiday, when our antihero miraculously arrives here after his habitualaccident-ridden adventures. There's even time for a doze in the sun before continuing into Villefranche's old town for a visit to the quirky Chapelle de St-Pierre (Quai de l'Amiral Ponchardier, €2). Jean Cocteau blanketed this harbourside church with murals of St Peter, cartoony fish and curvy lovers in 1957.

The 15.29 from Villefranche-sur-Mer rocks me gently westwards again, passing Nice, my starting point. Forty minutes later, I stroll out of Antibes station and down to the harbour. Ogling the super-size yachts on Millionaire's Quay is de rigueur. Roman Abramovich's Ecstasea is often in town; and until it was impounded a couple of years ago, Bernie Madoff's yacht, Bull, was berthed here, too.

The ramparts of Antibes Old Town lead to the Château Grimaldi, now home to the Musée Picasso (antibes-juanlespins.com, €6). In 1947 the Spanish master lived here, painting to the tune of swooping gulls and lapping waves. When he moved out, he donated much of his work to the French state, which in turn transformed the château into a small museum.

Monte Carlo. Photograph: Alamy

The late-afternoon sunshine sparkles off the waves as I head for Cap d'Antibes, a leafy protrusion of villas and beaches and yet another of the Riviera's uber-wealthy peninsulas poking majestically out to sea. Le Cap formed the glamorous 1920s backdrop for F Scott Fitzgerald's Tender is the Night, while nearby Juan-les-Pins lays claim to the invention of waterskiing and the suntan. A wander through the latter's pine-dotted central place, dotted with elderly men playing pétanque, and I'm keen to spend my summers working on my oeuvre here, too.

At 18.10, my pass takes me on a 13-minute zip to Cannes. I find a stroll along the town's seafront Croisette fun and frivolous rather than snooty or pretentious.

With my pass valid for another five hours, I consider continuing west. Instead I'm content with a seat on Mocca's (moccarestaurant.com) terrace opposite the Palais des Festivals, a killer mojito and dinner behind the port before catching the midnight train back to Nice.

The Riviera's rail line allowed me an action-packed day, with easy access to more of the Côte d'Azur than I first thought possible. Thanks to my Carte Isabelle, I managed to do it all on a tenner, too. Merci.

Essentials

Carte Isabelle passes cost €12 per day and are valid from 1 June to 30 September; Carte Isabelle Famille passes (€35/day, €80/three days for two adults and two under-16s) are valid year round. They offer unlimited train travel from Fréjus to Ventimiglia, and inland between Cannes and Grasse, and Nice and Tende. Passes can be purchased at any station along the Riviera